11 th Grade Maths

Solving 11th grade math problem 2:

Solve the given mathematical linear equation and find the values of the given variables.

x + 3y + 5z = 18

x + 5y + 3z = 18

3x + y + 5z = 18

Solution:

Let as the given equations be identified as follows.

x + 3y + 5z = 18 ----------- (i)

x + 5y + 3z = 18 ----------- (ii)

3x + y + 5z = 18 ----------- (iii)

Consider the above given equations (i) and (ii). Subtracting the equation (i) and (ii) we get

x + 3y + 5z = 18

x + 5y + 3z = 18

-2y – 2z = 0 ------------------ (iv)

Consider the above given equations (ii) and (iii). In the equation (ii) multiply with a numerical 3, we get

3x + 15y + 18z = 54

Subtracting the equation (ii) and (iii) we get

3x + 15y + 18z = 54

3x + y + 5z = 18

14y + 4z = 36------------------- (v)

Consider the above equations (iv) and (v). In the equation (iv) multiply with the numerical 7, we get

-14y - 14z = 0

Subtract the equation (iv) and (v) we get

-14y - 14z = 0

14y + 4z = 36

18y = 36

Y = 2

Substitute y = 2 in (v) we get

14(2) + 4z = 36

28 + 4z = 36

z = 2

Substitute z = 2, y = 2 in (iii) we get

3x + 2 + 10 = 36

3x + 12 = 36

z = 2

Answers of a given algebraic variables are x = 2, y = 2, z = 2.

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